A chamber designed for 7.62X51 will handle a .308 fine. The converse is not true. My .308 bolt guns require real .308 made by Federal or Winchester. A 7.62X51 will not settle into the chamber.
Factory rifles do not normally have this problem. If you have some custom tuned rifles, they may be limited to certain narrow range of cartridge lengths. Your slam fire problem may be for different reasons.
Here is a widely-cited article on the arcane subject you may find interesting:
http://www.fulton-armory.com/308.htmA Remington 700PSS is a factory rifle except for having Vias tune the trigger. I'm not putting any more 7.62X51 NATO in THAT rifle. If/When I purchase an M1A in .308, I'll give that stock of ammo another chance.